Realtime auto keying framing on the timeline don't work as expected on blender 2.81
If you need to record an animation on the fly, you have to start the playback first. So that time goes on in Blender's point of view and it can record what you each frame passing by:



Without that, time isn't involved, only the frame under your playhead can be keyed, and it will only do so when a transform is validated (like when you move your object somewhere and release your mouse button to confirm).

Hopefully this is just what you need.